The high diversity of HLA binding preferences has been driven by the sequence diversity of short segments of relevant pathogenic proteins presented by HLA molecules to the immune system. To identify possible commonalities in HLA binding preferences, we quantify these using a novel measure termed "targeting efficiency," which captures the correlation between HLA-peptide binding affinities and the conservation of the targeted proteomic regions. Analysis of targeting efficiencies for 95 HLA class I alleles over thousands of human proteins and 52 human viruses indicates that HLA molecules preferentially target conserved regions in these proteomes, although the arboviral Flaviviridae are a notable exception where nonconserved regions are preferentially targeted by most alleles. HLA-A alleles and several HLA-B alleles that have maintained close sequence identity with chimpanzee homologues target conserved human proteins and DNA viruses such as Herpesviridae and Adenoviridae most efficiently, while all HLA-B alleles studied efficiently target RNA viruses. These patterns of host and pathogen specialization are both consistent with coevolutionary selection and functionally relevant in specific cases; for example, preferential HLA targeting of conserved proteomic regions is associated with improved outcomes in HIV infection and with protection against dengue hemorrhagic fever. Efficiency analysis provides a novel perspective on the coevolutionary relationship between HLA class I molecular diversity, self-derived peptides that shape T-cell immunity through ontogeny, and the broad range of viruses that subsequently engage with the adaptive immune response.